Reasoning

Glossary

First-order Logic :

A formal logic system in mathematics distinguished from propositional logic by its use of quantified variables

Deductive Reasoning :

The process of reasoning from one or more general statements (premises) to reach a logic conclusion

Tableaux :

A proof procedure for formulas of first-order logic based on tree expansion

Resolution :

A proof procedure for formulas of first-order logic based on a set of inference rules for clauses

Definition

When considering logical reasoning, it is often divided into three basic paradigms: deductive, inductive, and abductive reasoning. Deductive reasoning concerns what follows necessarily from the given premises (if α, then β) in a top-down approach, while inductive reasoning, the opposite of deductive reasoning, tries to derive a reliable generalization from observations in a bottom-up approach. Abductive reasoning is seeking the explanation for given rules and conclusions (if α → β and β, then perhaps α.) For each of them,...